Question

find the inverse of the function: $f(x) = 7x - 2$

select one:
a. $f^{-1}(x) = \frac{x - 2}{-7}$
b. $f^{-1}(x) = \frac{x - 2}{7}$
c. $f^{-1}(x) = -\frac{x + 2}{7}$
d. $f^{-1}(x) = \frac{x + 2}{7}$

Explanation:

Step1: Replace $f(x)$ with $y$

$y = 7x - 2$

Step2: Swap $x$ and $y$

$x = 7y - 2$

Step3: Solve for $y$, isolate $7y$

$7y = x + 2$

Step4: Solve for $y$, divide by 7

$y = \frac{x + 2}{7}$

Step5: Replace $y$ with $f^{-1}(x)$

$f^{-1}(x) = \frac{x + 2}{7}$

Answer:

D. $f^{-1}(x) = \frac{x + 2}{7}$